Analysis of a mode-I crack in a one-dimensional orthorhombic quasicrystal strip

A mode-I crack in a one-dimensional (1D) orthorhombic quasicrystal (QC) strip under in-plane phonon and phason stress loading is considered. Fourier transforms are applied to reduce the mixed boundary value problem of the mode-I crack to solving a system of simultaneous singular integral equations. Asymptotic expressions of the phonon and phason stresses and displacement fields near the crack tips have been obtained in an explicit form. The crack-tip singularities of the mode-I crack have been investigated and the intensity factors of the stresses in the phonon and phason fields are derived explicitly. The stress intensity factors (SIFs) and the hoop stress intensity factors (HSIFs) have been determined to investigate the effect of the geometric size and the crack kinking phenomenon. The effect of the thickness ratio of the cracked strip on the SIFs and energy release rates has been investigated. When the thickness of the cracked strip becomes infinite large, the results obtained for the crack problem can be reduced to the analytic solution for a mode-I crack in an infinite 1D orthorhombic QC media.

Automated summary

This paper investigates the behavior of a mode-I crack in a one-dimensional orthorhombic quasicrystal strip under in-plane phonon and phason stress loading. By applying Fourier transforms and solving a system of simultaneous singular integral equations, asymptotic expressions of the stress and displacement fields near the crack tips are obtained. The crack tip singularities and stress intensity factors are analyzed, and the effects of geometric size and crack kinking phenomenon are studied. The influence of the thickness ratio of the cracked strip on stress intensity factors and energy release rates is also investigated.